Problem: Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in a so that it becomes a good array. Can you help him?

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into 2 subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 2000) — the elements of the array a.

Output

The first line should contain the minimum number of elements you need to remove.

The second line should contain the indices of the elements you're removing, separated by spaces.

We can show that an answer always exists. If there are multiple solutions, you can print any.

Examples

Input


4
6 3 9 12


Output


1
2

Input


2
1 2


Output


0

Note

In the first example, you can partition the array into [6,9] and [3,12], so you must remove at least 1 element. Removing 3 is sufficient.

In the second example, the array is already good, so you don't need to remove any elements.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
 
import java.math.*;
import java.awt.Point;
 
public class Main {
    static final long MOD = 1000000007L;
    //static final long MOD2 = 1000000009L;
    //static final long MOD = 998244353L;
    //static final long INF = 500000000000L;
    static final int INF =   1000000005;
    static final int NINF = -1000000005;
    //static final long NINF = -1000000000000000000L;
    static FastScanner sc;
    static PrintWriter pw;
    static final int[][] dirs = {{-1,0},{1,0},{0,-1},{0,1}};
 
 
    static final int MO = 1200;
    
    public static void main(String[] args) {
        sc = new FastScanner();
        pw = new PrintWriter(System.out);
 
        /*int N = sc.ni();
        int Q = sc.ni();
        int[] A = sc.intArray(N, 0);
        boolean[] sieve = new boolean[100001];
        Arrays.fill(sieve,true);
        for (int i = 2; i <= 100000; i++) {
            if (sieve[i]) {
                for (int j = 2*i; j <= 100000; j += i) {
                    sieve[j] = false;
                }
            }
        }
        ArrayList<Integer> primes = new ArrayList<Integer>();
        for (int i = 2; i <= 316; i++) {
            if (sieve[i]) primes.add(i);
        }
        int P = primes.size();

        ArrayDeque<Integer>[] divs = new ArrayDeque[100001];
        for (int i = 0; i < N; i++) {
            for (int p: primes) {
                if (A[i]%p == 0) {
                    if (divs[p]==null) divs[p] = new ArrayDeque<Integer>();
                    divs[p].add(i);
                }
            }
            if (A[i] > 316 && sieve[A[i]]) {
                if (divs[A[i]]==null) divs[A[i]] = new ArrayDeque<Integer>();
                divs[A[i]].add(i);
            }
        }

        int[][] table = new int[17][N];
        int R = N;
        for (int L = N-1; L >= 0; L--) {
            for (int p: primes) {
                if (A[L]%p==0) {
                    while (divs[p].peekLast() > L) {
                        R = Math.min(R,divs[p].pollLast());
                    }
                }
            }
            if (A[L] > 316 && sieve[A[L]]) {
                while (divs[A[L]].peekLast() > L) {
                    R = Math.min(R,divs[A[L]].pollLast());
                }
            }
            table[0][L] = R;
        }

        for (int i = 1; i < 17; i++) {
            for (int j = 0; j < N; j++) {
                int next = table[i-1][j];
                if (next < N)
                    table[i][j] = table[i-1][next];
                else
                    table[i][j] = N;
            }
        }

        for (int q = 0; q < Q; q++) {
            int ql = sc.ni()-1;
            int qr = sc.ni()-1;
            
            int lo = 1;
            int hi = 100000;
            while (lo < hi) {
                int m = (lo+hi)/2;
                int cur = ql;
                for (int bit = 16; bit >= 0; bit--) {
                    if ((m&(1<<bit)) > 0) {
                        cur = table[bit][cur];
                        if (cur==N) break;
                    }
                }
                if (cur > qr) {
                    hi = m;
                } else {
                    lo = m+1;
                }
            }
            pw.println(lo);
        }*/

        int N = sc.ni();
        int[] A = sc.intArray(N,0);
        while (true) {
            boolean allEven = true;
            for (int i = 0; i < N; i++) {
                if (A[i]%2==1) {
                    allEven = false;
                    break;
                }
            }
            if (allEven) {
                for (int i = 0; i < N; i++) A[i] /= 2;
            } else {
                break;
            }
        }
        int sum = 0;
        for (int i = 0; i < N; i++) sum += A[i];

        int odd = -1;
        for (int i = 0; i < N; i++) {
            if (A[i]%2==1) {
                odd = i;
                break;
            }
        }

        if (sum % 2 == 1) {
            pw.println(0);
        } else {
            int T = sum/2;
            boolean[][] dp = new boolean[N+1][T+1];
            dp[0][0] = true;
            for (int i = 1; i <= N; i++) {
                for (int j = 0; j <= T; j++) {
                    dp[i][j] = dp[i-1][j];
                    if (A[i-1] <= j) {
                        dp[i][j] |= dp[i-1][j-A[i-1]];
                    }
                }
            }

            if (dp[N][T]) {
                pw.println(1);
                pw.println(odd+1);
            } else {
                pw.println(0);
            }
        }

        pw.close();
    }
 
    public static void sort(int[] arr) {
        Random rgen = new Random();
        for (int i = 0; i < arr.length; i++) {
            int r = rgen.nextInt(arr.length);
            int temp = arr[i];
            arr[i] = arr[r];
            arr[r] = temp;
        }
        Arrays.sort(arr);
    }
 
    public static void sort(long[] arr) {
        Random rgen = new Random();
        for (int i = 0; i < arr.length; i++) {
            int r = rgen.nextInt(arr.length);
            long temp = arr[i];
            arr[i] = arr[r];
            arr[r] = temp;
        }
        Arrays.sort(arr);
    }
 
    //Sort an array (immune to quicksort TLE)
    public static void sort(int[][] arr) {
        Random rgen = new Random();
        for (int i = 0; i < arr.length; i++) {
            int r = rgen.nextInt(arr.length);
            int[] temp = arr[i];
            arr[i] = arr[r];
            arr[r] = temp;
        }
        Arrays.sort(arr, new Comparator<int[]>() {
            @Override
            public int compare(int[] a, int[] b) {
                int ablock = a[0]/MO;
                int bblock = b[0]/MO;
                if (ablock != bblock)
                    return ablock-bblock;
                else
                    return a[1]-b[1];
            }
        });
    }
    
    public static void sort(long[][] arr) {
        Random rgen = new Random();
        for (int i = 0; i < arr.length; i++) {
            int r = rgen.nextInt(arr.length);
            long[] temp = arr[i];
            arr[i] = arr[r];
            arr[r] = temp;
        }
        Arrays.sort(arr, new Comparator<long[]>() {
            @Override
            public int compare(long[] a, long[] b) {
                if (a[0] > b[0])
                    return 1;
                else if (a[0] < b[0])
                    return -1;
                else
                    return 0;
                //Ascending order.
            }
        });
    }
 
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in), 32768);
            st = null;
        }
 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int ni() {
            return Integer.parseInt(next());
        }
 
        int[][] graph(int N, int[][] edges) {
            int[][] graph = new int[N][];
            int[] sz = new int[N];
            for (int[] e: edges) {
                sz[e[0]] += 1;
                sz[e[1]] += 1;
            }
            for (int i = 0; i < N; i++) {
                graph[i] = new int[sz[i]];
            }
            int[] cur = new int[N];
            for (int[] e: edges) {
                graph[e[0]][cur[e[0]]] = e[1];
                graph[e[1]][cur[e[1]]] = e[0];
                cur[e[0]] += 1;
                cur[e[1]] += 1;
            }
            return graph;
        }
 
        int[] intArray(int N, int mod) {
            int[] ret = new int[N];
            for (int i = 0; i < N; i++)
                ret[i] = ni()+mod;
            return ret;
        }
 
        long nl() {
            return Long.parseLong(next());
        }
 
        long[] longArray(int N, long mod) {
            long[] ret = new long[N];
            for (int i = 0; i < N; i++)
                ret[i] = nl()+mod;
            return ret;
        }
 
        double nd() {
            return Double.parseDouble(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}